Abstract

۱٫ Introduction

۲٫ Model definition

۳٫ Model creation

۴٫ Simulation process

۵٫ Conclusions

Acknowledgements

References

Abstract

     Representing any type of living tissue in digital form is a complex and demanding problem due to its heterogeneous structure as well as different issues that can be encountered during such transition. Usually, to ensure faster computation times, models are simplified, i.e. by averaging available parameters. Such an approach can result in omitting essential features and, consequently, lead to lower accuracy of obtained results.

     In simulations, bioelectromagnetism uses a different approach to numerical calculations. Additionally, models are used to represent the phenomena they describe. This article presents an approach to tissue representation in the field of bioelectromagnetic simulations and research, which is the result of work carried out by the authors in this field in recent years.

     The description of the model is widely discussed in the paper, taking into account the problem of numerical uncertainty, reliability, averaging or the adopted geometry. Each concept is presented in the examples, along with the possible level of minimization of the impact on the simulation results. The work also includes an exemplary model with a parametric description of tissues and the impact of these problems on the actual results. We present an analysis showing which parameters are essential for tissue modelling, how the complexity of a model influences a simulation and how using different tissue models can impact the relation between total simulation time and output effectiveness. The simulation process was based on a large-scale cloud computing environment with the presented design, simulation and optimization solution, one of the many available.

Introduction

The problem of human tissue representation in digital form, used for simulations in mathematics, mechanics or electrical engineering, has been discussed in the scientific literature since the first half of the 20th century. At the same time, modelling problems with the use of computing machines at that time did not appear until the 1960s. In the beginning, the central theme of the described research was the transfer of the biological state to a mathematical notation that would allow the definition of individual organs, unified tissues or even entire objects constituting a simulation model of the human body. Thanks to an increasingly detailed understanding of anatomy as well as more complex mathematical functions and technological development, the quality of the simulations, models and their digital representation have improved significantly.

One of the first similarly described works, when it comes to the subject of tissue modelling, is [1]. In this case, the numerical model for the capillary–tissue system was defined, which is responsible for oxygen transportation in cerebral grey matter. The presented definition assumes significant simplifications in overall representation instead of focusing on defining the problem in a controlled way and propose, above all, an understanding of the functioning of the biological oxygen transport system. Another example, which uses the mathematical model, uses the finite element method to visualize the mesh describing human aortic valve leaflets [2]. A completely different yet also numerical approach is described in [3]. The authors present the reconstruction of the mathematical model of the human chest on the basis of the potential from the electrodes using the inverse solution.

Conclusions

     In the course of the research conducted in recent years (the results of which have been presented here), methodologies for the modelling of biological objects (tissues) in bioelectromagnetic problems have been developed. The problem of computer imaging of tissues is highly complex, and it is not possible to accurately reproduce them on a micro-scale. Treatment of tissues ‘‘molecularly’’ is almost impossible or involves much computational effort.

     Determining the relationship between such a precisely mapped model mesh, taking into account the concept of the variability, the existing environment, building a mathematical model or uncertainty, is currently beyond the computational capabilities of even supercomputers. Additionally, the issue of detail and scale of the problem should be considered for each such application.

     It is the given fact that increasing accuracy of the model will result in similar relations in the obtained results, which may include previously unaccounted cases and threats, e.g. for humans — whether in therapy or in an electronic device that a human will have to deal with. At the same time, it will result in increasing computation time and problems with preparing actually executable scenarios.